Diagonalization of two quaternion tensors with applications

The generalized singular value decomposition for two quaternion tensors via t-product is investigated in this paper. Based on the decomposition, we design an algorithm to compute the simultaneous decompositions. Due to the strong correlation between adjacent pixel pairs, it is essential for video encryption techniques to diminish this correlation in order to improve security. Considering the need to process multiple video simultaneously to utilize computing resources more efficiently, this paper focuses on the simultaneous encryption and decryption of two color videos and finds that this method can further lower the average correlation coefficients among the three channels of the encrypted video frames in the horizontal, vertical, and diagonal directions compared with some existed works. Also this approach requires fewer keys for the encryption and decryption of the two videos compared to encrypting and decrypting them separately, making key management more convenient and efficient. Our tensor decomposition-based method demonstrates enhanced resistance to attacks while achieving more efficient resource utilization.